diff --git a/doc/src/compute_orientorder_atom.rst b/doc/src/compute_orientorder_atom.rst index 01535aa880..08153fe496 100644 --- a/doc/src/compute_orientorder_atom.rst +++ b/doc/src/compute_orientorder_atom.rst @@ -49,7 +49,7 @@ For each atom, :math:`Q_\ell` is a real number defined as follows: .. math:: - \bar{Y}_{\ell m} = & \frac{1}{nnn}\sum_{j = 1}^{nnn} Y_{\ell m}\bigl( \theta( {\bf r}_{ij} ), \phi( {\bf r}_{ij} ) \bigr) \\ + \bar{Y}_{\ell m} = & \frac{1}{nnn}\sum_{j = 1}^{nnn} Y_{\ell m}\bigl( \theta( \mathbf{r}_{ij} ), \phi( \mathbf{r}_{ij} ) \bigr) \\ Q_\ell = & \sqrt{\frac{4 \pi}{2 \ell + 1} \sum_{m = -\ell }^{m = \ell } \bar{Y}_{\ell m} \bar{Y}^*_{\ell m}} The first equation defines the local order parameters as averages diff --git a/doc/src/compute_sna_atom.rst b/doc/src/compute_sna_atom.rst index 2572093499..d0c76dd4ca 100644 --- a/doc/src/compute_sna_atom.rst +++ b/doc/src/compute_sna_atom.rst @@ -204,7 +204,7 @@ components summed separately for each LAMMPS atom type: .. math:: - -\sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j} }}{\partial {\bf r}_i} + -\sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j} }}{\partial \mathbf{r}_i} The sum is over all atoms *i'* of atom type *I*\ . For each atom *i*, this compute evaluates the above expression for each direction, each @@ -216,7 +216,7 @@ derivatives: .. math:: - -{\bf r}_i \otimes \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}}}{\partial {\bf r}_i} + -\mathbf{r}_i \otimes \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}}}{\partial \mathbf{r}_i} Again, the sum is over all atoms *i'* of atom type *I*\ . For each atom *i*, this compute evaluates the above expression for each of the six diff --git a/doc/src/fix_gld.rst b/doc/src/fix_gld.rst index ba26f7a51b..8c24275cb4 100644 --- a/doc/src/fix_gld.rst +++ b/doc/src/fix_gld.rst @@ -60,9 +60,9 @@ With this fix active, the force on the *j*\ th atom is given as .. math:: - {\bf F}_{j}(t) = & {\bf F}^C_j(t)-\int \limits_{0}^{t} \Gamma_j(t-s) {\bf v}_j(s)~\text{d}s + {\bf F}^R_j(t) \\ + \mathbf{F}_{j}(t) = & \mathbf{F}^C_j(t)-\int \limits_{0}^{t} \Gamma_j(t-s) \mathbf{v}_j(s)~\text{d}s + \mathbf{F}^R_j(t) \\ \Gamma_j(t-s) = & \sum \limits_{k=1}^{N_k} \frac{c_k}{\tau_k} e^{-(t-s)/\tau_k} \\ - \langle{\bf F}^R_j(t),{\bf F}^R_j(s)\rangle = & \text{k$_\text{B}$T} ~\Gamma_j(t-s) + \langle\mathbf{F}^R_j(t),\mathbf{F}^R_j(s)\rangle = & \text{k$_\text{B}$T} ~\Gamma_j(t-s) Here, the first term is representative of all conservative (pairwise, bonded, etc) forces external to this fix, the second is the temporally diff --git a/doc/src/fix_lb_fluid.rst b/doc/src/fix_lb_fluid.rst index a461175f71..e49831986b 100644 --- a/doc/src/fix_lb_fluid.rst +++ b/doc/src/fix_lb_fluid.rst @@ -130,7 +130,7 @@ calculated as: .. math:: - {\bf F}_{j \alpha} = \gamma \left({\bf v}_n - {\bf u}_f \right) \zeta_{j\alpha} + \mathbf{F}_{j \alpha} = \gamma \left(\mathbf{v}_n - \mathbf{u}_f \right) \zeta_{j\alpha} where :math:`\mathbf{v}_n` is the velocity of the MD particle, :math:`\mathbf{u}_f` is the fluid velocity interpolated to the particle diff --git a/doc/src/fix_pimd.rst b/doc/src/fix_pimd.rst index f29124e9aa..3ee11014bf 100644 --- a/doc/src/fix_pimd.rst +++ b/doc/src/fix_pimd.rst @@ -101,7 +101,7 @@ by the following equations: .. math:: - Z = & \int d{\bf q} d{\bf p} \cdot \textrm{exp} [ -\beta H_{eff} ] \\ + Z = & \int d\mathbf{q} d\mathbf{p} \cdot \textrm{exp} [ -\beta H_{eff} ] \\ H_{eff} = & \bigg(\sum_{i=1}^P \frac{p_i^2}{2M_i}\bigg) + V_{eff} \\ V_{eff} = & \sum_{i=1}^P \bigg[ \frac{mP}{2\beta^2 \hbar^2} (q_i - q_{i+1})^2 + \frac{1}{P} V(q_i)\bigg] diff --git a/doc/src/fix_pimd_bosonic.rst b/doc/src/fix_pimd_bosonic.rst index 67dd60ed39..e54e87e8fb 100644 --- a/doc/src/fix_pimd_bosonic.rst +++ b/doc/src/fix_pimd_bosonic.rst @@ -97,7 +97,7 @@ inverse temperature :math:`\beta` is given by :ref:`(Tuckerman) .. math:: - Z \propto \int d{\bf q} \cdot \frac{1}{N!} \sum_\sigma \textrm{exp} [ -\beta \left( E^\sigma + V \right) ]. + Z \propto \int d\mathbf{q} \cdot \frac{1}{N!} \sum_\sigma \textrm{exp} [ -\beta \left( E^\sigma + V \right) ]. Here, :math:`V` is the potential between different particles at the same imaginary time slice, which is the same for bosons and distinguishable diff --git a/doc/src/pair_aip_water_2dm.rst b/doc/src/pair_aip_water_2dm.rst index 65f2e4d912..b7c33e9c86 100644 --- a/doc/src/pair_aip_water_2dm.rst +++ b/doc/src/pair_aip_water_2dm.rst @@ -57,8 +57,8 @@ materials as described in :ref:`(Feng1) ` and :ref:`(Feng2) `. \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ - \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ - \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ + \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_i)^2 \\ + \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + diff --git a/doc/src/pair_ilp_graphene_hbn.rst b/doc/src/pair_ilp_graphene_hbn.rst index 7fa7d6800f..e50509497f 100644 --- a/doc/src/pair_ilp_graphene_hbn.rst +++ b/doc/src/pair_ilp_graphene_hbn.rst @@ -48,8 +48,8 @@ in :ref:`(Kolmogorov) `. \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ - \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ - \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ + \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_i)^2 \\ + \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + diff --git a/doc/src/pair_ilp_tmd.rst b/doc/src/pair_ilp_tmd.rst index 133e5f9093..f486f73c69 100644 --- a/doc/src/pair_ilp_tmd.rst +++ b/doc/src/pair_ilp_tmd.rst @@ -45,8 +45,8 @@ as described in :ref:`(Ouyang7) ` and :ref:`(Jiang) `. \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ - \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ - \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ + \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_i)^2 \\ + \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + @@ -67,7 +67,7 @@ calculating the normals. normal vectors used for graphene and h-BN is no longer valid for TMDs. In :ref:`(Ouyang7) `, a new definition is proposed, where for each atom `i`, its six nearest neighboring atoms belonging to the same - sub-layer are chosen to define the normal vector `{\bf n}_i`. + sub-layer are chosen to define the normal vector `\mathbf{n}_i`. The parameter file (e.g. TMD.ILP), is intended for use with *metal* :doc:`units `, with energies in meV. Two additional parameters, diff --git a/doc/src/pair_kolmogorov_crespi_full.rst b/doc/src/pair_kolmogorov_crespi_full.rst index 1a4706dd6f..2af56cbf9b 100644 --- a/doc/src/pair_kolmogorov_crespi_full.rst +++ b/doc/src/pair_kolmogorov_crespi_full.rst @@ -37,8 +37,8 @@ No simplification is made, E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ V_{ij} = & e^{-\lambda (r_{ij} -z_0)} \left [ C + f(\rho_{ij}) + f(\rho_{ji}) \right ] - A \left ( \frac{r_{ij}}{z_0}\right )^{-6} \\ - \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij}\cdot {\bf n}_{i})^2 \\ - \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij}\cdot {\bf n}_{j})^2 \\ + \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij}\cdot \mathbf{n}_{i})^2 \\ + \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij}\cdot \mathbf{n}_{j})^2 \\ f(\rho) & = e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} { (\rho/\delta) }^{2n} It is important to have a sufficiently large cutoff to ensure smooth diff --git a/doc/src/pair_mgpt.rst b/doc/src/pair_mgpt.rst index 13a4bcb079..e492e555ac 100644 --- a/doc/src/pair_mgpt.rst +++ b/doc/src/pair_mgpt.rst @@ -33,7 +33,7 @@ elemental bulk material in the form .. math:: - E_\mathrm{tot}({\bf R}_1 \ldots {\bf R}_N) = NE_\mathrm{vol}(\Omega ) + E_\mathrm{tot}(\mathbf{R}_1 \ldots \mathbf{R}_N) = NE_\mathrm{vol}(\Omega ) + \frac{1}{2} \sum _{i,j} \mbox{}^\prime \ v_2(ij;\Omega ) + \frac{1}{6} \sum _{i,j,k} \mbox{}^\prime \ v_3(ijk;\Omega ) + \frac{1}{24} \sum _{i,j,k,l} \mbox{}^\prime \ v_4(ijkl;\Omega ) diff --git a/doc/src/pair_saip_metal.rst b/doc/src/pair_saip_metal.rst index 098edff916..211e5e9359 100644 --- a/doc/src/pair_saip_metal.rst +++ b/doc/src/pair_saip_metal.rst @@ -45,8 +45,8 @@ potential (ILP) potential for hetero-junctions formed with hexagonal \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ - \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ - \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ + \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_i)^2 \\ + \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + @@ -63,8 +63,8 @@ calculating the normals. .. note:: To account for the isotropic nature of the isolated gold atom - electron cloud, their corresponding normal vectors (`{\bf n}_i`) are - assumed to lie along the interatomic vector `{\bf r}_ij`. Notably, this + electron cloud, their corresponding normal vectors (`\mathbf{n}_i`) are + assumed to lie along the interatomic vector `\mathbf{r}_ij`. Notably, this assumption is suitable for many bulk material surfaces, for example, for systems possessing s-type valence orbitals or metallic surfaces, whose valence electrons are mostly